Tweak my study habits.
April 10, 2013 8:47 AM Subscribe
I'm taking Calc II at a community college and I'm not getting the grades I want. Studying 10 hours everyday a week in advance only got me an 84% on the first test. It is clear that I'm doing something wrong, but what is it? Help me tweak my study habits before the second test!
When I took Algebra, Trig, and Pre-Calculus, there was a positive correlation between the amount of time I studied and the grades I received. Studying all day, everyday, in advance was the trick for me. However, I'm dismayed at why this isn't working anymore. Perhaps the subject got harder and I need even more time to study? Or maybe I need to be wiser about how I study instead of blindly throwing more time into studying?
To get a more spot-on answer, let me tell you how I go about it. My professor assigns a ton of homework from the textbook. It takes me a day to finish one section of homework and each consists of a few easy problems, some intermediately hard problems, and some incredibly difficult special case problems that he doesn't even lecture on and probably won't test. I painstakingly do every problem and utilize the campus' free tutoring. I figure if I could do the hard stuff, I can do anything. Right?
So I do my homework for the majority of the week. Then a few days before the test I redo them to make sure I got this stuff down step-by-step via memory. I work on the study guide right before the test. And then I take the test. To my delight, my professor's testing style is surprisingly simple. He only tests the bare basics. No bells and whistles. The homework was way harder so I thought I was going to ace this until I started taking it.
I lacked some basic understanding, but how? I legibly did the damn homework twice and reviewed the material! When I got my test back, I loss 4% to careless mistakes despite triple-checking. The fact that I put incredible effort and time into this makes me feel even more stupid. Maybe all that homework hinders me instead of help and I should bullshit them to make time for studying basic concepts. Maybe all that tutoring and homework gave me a false sense of security so I overlook things. I'm in distress and I don't know how to proceed. I need permission to change the study habit that worked so well in the past. Any thoughts?
When I took Algebra, Trig, and Pre-Calculus, there was a positive correlation between the amount of time I studied and the grades I received. Studying all day, everyday, in advance was the trick for me. However, I'm dismayed at why this isn't working anymore. Perhaps the subject got harder and I need even more time to study? Or maybe I need to be wiser about how I study instead of blindly throwing more time into studying?
To get a more spot-on answer, let me tell you how I go about it. My professor assigns a ton of homework from the textbook. It takes me a day to finish one section of homework and each consists of a few easy problems, some intermediately hard problems, and some incredibly difficult special case problems that he doesn't even lecture on and probably won't test. I painstakingly do every problem and utilize the campus' free tutoring. I figure if I could do the hard stuff, I can do anything. Right?
So I do my homework for the majority of the week. Then a few days before the test I redo them to make sure I got this stuff down step-by-step via memory. I work on the study guide right before the test. And then I take the test. To my delight, my professor's testing style is surprisingly simple. He only tests the bare basics. No bells and whistles. The homework was way harder so I thought I was going to ace this until I started taking it.
I lacked some basic understanding, but how? I legibly did the damn homework twice and reviewed the material! When I got my test back, I loss 4% to careless mistakes despite triple-checking. The fact that I put incredible effort and time into this makes me feel even more stupid. Maybe all that homework hinders me instead of help and I should bullshit them to make time for studying basic concepts. Maybe all that tutoring and homework gave me a false sense of security so I overlook things. I'm in distress and I don't know how to proceed. I need permission to change the study habit that worked so well in the past. Any thoughts?
Your professor wants you to get good grades. It looks good for professors to have high-achieving students, so figuring out a strategy for finding what you're missing will be as important to him as it is to you.
posted by xingcat at 8:57 AM on April 10, 2013 [3 favorites]
posted by xingcat at 8:57 AM on April 10, 2013 [3 favorites]
If only 4% is to silly mistakes, what did you lose the other 12% to? With math problems, it is more important to understand the concepts, rather than answers to specific questions. It is possible that you spent a lot of time memorizing the answers to the given questions rather than understanding how to apply the solutions to many different questions. I agree with the suggestion of talking to the professor - perhaps you can spend more time doing many easy problems (that you will be tested on) rather than spending a lot of time understanding very difficult problems. You could also ask your professor/tutors for tips on ways to double check your solutions.
posted by fermezporte at 8:59 AM on April 10, 2013 [1 favorite]
posted by fermezporte at 8:59 AM on April 10, 2013 [1 favorite]
Do your homework. Do all your homework. Then find extra problems to work on. Now that you've had one test, you have an idea of your prof's testing style. Do extra problems that look like the kinds of questions he will ask.
There is always a chance of losing marks to "careless" mistakes. It sucks but most people make mistakes like this - including most math professors I've had! The good ones invited us to correct their mistakes.
Also, what chickenmagazine said. That is solid advice. Make sure you understand what you were missing from the test.
posted by fullerenedream at 9:02 AM on April 10, 2013
There is always a chance of losing marks to "careless" mistakes. It sucks but most people make mistakes like this - including most math professors I've had! The good ones invited us to correct their mistakes.
Also, what chickenmagazine said. That is solid advice. Make sure you understand what you were missing from the test.
posted by fullerenedream at 9:02 AM on April 10, 2013
Best answer: I am not a math teacher, but I teach a quantitative subject at the college level (physics/astronomy, if it matters). I see a lot of students who come in and think that they can just power through (do ALL the problems, redo all the problems before an exam). These are students for whom this strategy worked very well in high school (and maybe even early college). There's a point at which this strategy starts to fail; this is often when the concepts that are being taught get more complicated.
I hesitate to suggest you change a strategy that has worked for you in the past, but here's what I often suggest to my students: instead of re-doing your homeworks, take a look at the homeworks that you've gotten back. Make sure you understand why you got things wrong and, almost as importantly, why you got things right. Then, try to put yourself in your professor's head: why did (s)he ask these questions? What was the goal in assigning these problems? What is the central idea that (s)he was hoping I'd learn from doing these problems? If you can't answer those questions, I might suggest that you don't understand the central ideas (the ideas most likely to be on the test) well enough. If you can answer those questions, go practice on new problems that test your understanding of the ideas. Re-doing old homeworks "blindly" usually doesn't help to build/test understanding.
For me, I really don't care about your ability to do math (this is where what I teach may differ from your math class). I care about your ability to understand quantitative ideas. You have to use math to understand quantitative ideas, but little math mistakes matter much less to me (both in points and in broader ways) than understanding the ideas.
posted by Betelgeuse at 9:02 AM on April 10, 2013 [12 favorites]
I hesitate to suggest you change a strategy that has worked for you in the past, but here's what I often suggest to my students: instead of re-doing your homeworks, take a look at the homeworks that you've gotten back. Make sure you understand why you got things wrong and, almost as importantly, why you got things right. Then, try to put yourself in your professor's head: why did (s)he ask these questions? What was the goal in assigning these problems? What is the central idea that (s)he was hoping I'd learn from doing these problems? If you can't answer those questions, I might suggest that you don't understand the central ideas (the ideas most likely to be on the test) well enough. If you can answer those questions, go practice on new problems that test your understanding of the ideas. Re-doing old homeworks "blindly" usually doesn't help to build/test understanding.
For me, I really don't care about your ability to do math (this is where what I teach may differ from your math class). I care about your ability to understand quantitative ideas. You have to use math to understand quantitative ideas, but little math mistakes matter much less to me (both in points and in broader ways) than understanding the ideas.
posted by Betelgeuse at 9:02 AM on April 10, 2013 [12 favorites]
What I would do as part of test prep is to do some of the textbook problems at the end of each section that the Prof didn't assign. I would especially focus on the problems with answers at the back of the book. The point is to make what you've learned has gelled and the problem solving approach you picked up from lecture/assigned homework problems can be generalized. If you're able to do that, then work on trying to figure out how you're making careless mistakes.
The key isn't to blindly memorize the algorithm to solve the assigned problems but to be able to generalize the approach to other problems.
posted by scalespace at 9:03 AM on April 10, 2013 [1 favorite]
The key isn't to blindly memorize the algorithm to solve the assigned problems but to be able to generalize the approach to other problems.
posted by scalespace at 9:03 AM on April 10, 2013 [1 favorite]
One other key thing (that I see others have mentioned): Go talk to your professor! I can't tell you how long it took me to learn this very important lesson when I was a student and how few of my students have yet to learn it. Particularly if you have trouble doing the type of synthesis I describe above (i.e. "What central idea is the professor trying to teach me?"), this can be very helpful. Any professor worth their salt is thrilled to talk to students who are trying to do better and understand more.
posted by Betelgeuse at 9:06 AM on April 10, 2013 [3 favorites]
posted by Betelgeuse at 9:06 AM on April 10, 2013 [3 favorites]
At higher levels, math is really much closer to chess: it's a game of pattern recognition. Being able to recognize when you have an integral that calls for integration by parts, or when a trig substitution will be useful, etc. is the key to these problems.
It sounds like you're doing okay on the technical/computational side of things, aside from the silly mistakes. So, the way you should practice to build your pattern recognition skills is to do problems and focus on identifying why a specific technique fits that problem. If it's integration by parts, what clued you in? If it's close to something that is familiar, is there a substitution you can use to get it to look like that?
posted by philosophygeek at 9:08 AM on April 10, 2013
It sounds like you're doing okay on the technical/computational side of things, aside from the silly mistakes. So, the way you should practice to build your pattern recognition skills is to do problems and focus on identifying why a specific technique fits that problem. If it's integration by parts, what clued you in? If it's close to something that is familiar, is there a substitution you can use to get it to look like that?
posted by philosophygeek at 9:08 AM on April 10, 2013
I wonder if you're really deeply understanding the concepts in the section. Your comment about "the really hard problems that the professor doesn't even to bother to lecture on and won't be on the test"---typically, those are just slightly more interesting applications of the same concepts you used in the "easy" problems. E. g., instead of "use integration by parts to solve this integral", you are given a formula for marginal cost and then asked to find the total cost of selling 40 items, which requires you to (1) realize you need to compute an integral (2) correctly compute the integral using integration by parts (3) do something with the result when you're done.
So if the later HW problems seem useless and alien, you may need to work on synthesizing previous knowledge.
And agreed, go talk to your professor.
(I have taught calc II in the past and will again in the future. Like next fall.).
posted by leahwrenn at 9:09 AM on April 10, 2013 [3 favorites]
So if the later HW problems seem useless and alien, you may need to work on synthesizing previous knowledge.
And agreed, go talk to your professor.
(I have taught calc II in the past and will again in the future. Like next fall.).
posted by leahwrenn at 9:09 AM on April 10, 2013 [3 favorites]
Response by poster: I think this is important. I'm looking at my test and realize I made 8% of careless mistakes instead 4%. This is completely unacceptable.
It was the disk and shell method. I did the disk method just fine, but had some kind of brain fart when I set up the shell method. What mystifies me is that I didn't run into this problem on the homework. In fact, I considered it to be one of the concepts I had down. Could it be test anxiety? Maybe the homework gave me overconfidence causing me to overlook things.
I will definitely take the majority's advice and speak to my professor.
posted by squirtle at 9:31 AM on April 10, 2013
It was the disk and shell method. I did the disk method just fine, but had some kind of brain fart when I set up the shell method. What mystifies me is that I didn't run into this problem on the homework. In fact, I considered it to be one of the concepts I had down. Could it be test anxiety? Maybe the homework gave me overconfidence causing me to overlook things.
I will definitely take the majority's advice and speak to my professor.
posted by squirtle at 9:31 AM on April 10, 2013
Using resources external to class and the textbook may help you. I'm taking CalcI right now (and looking forward to CalcII and beyond), and when I'm struggling, I turn to youtube. Khan Academy and IntegralCalc videos have really helped me to solidify concepts in a way my professor and textbook could not. For example, I just couldn't wrap my head around limits. No matter how much I read the text or asked my prof. But after watching a video or two, it clicked.
posted by Cat Pie Hurts at 9:40 AM on April 10, 2013
posted by Cat Pie Hurts at 9:40 AM on April 10, 2013
I've had good success with a study group for a subject that I needed to do better in. Partly because other students processed answers and strategies differently, and I learned from them.
posted by theora55 at 9:51 AM on April 10, 2013 [2 favorites]
posted by theora55 at 9:51 AM on April 10, 2013 [2 favorites]
When you say "triple-checking," do you mean going back and redoing the work again (or going through it step-by-step) or do you mean looking critically at your answers?
For numerical questions, is your number positive or negative? Does that make sense? Is it a large large or small? Does that make sense?
For answers that are left in terms of variables and parameters, if you make one of the variables larger, does the answer change as you expect it to?
I agree with the advice above to go talk to the professor, who can help you focus your efforts so that you're spending the majority of your practice time working problems similar to those that are going to appear on the exam.
posted by BrashTech at 9:59 AM on April 10, 2013 [1 favorite]
For numerical questions, is your number positive or negative? Does that make sense? Is it a large large or small? Does that make sense?
For answers that are left in terms of variables and parameters, if you make one of the variables larger, does the answer change as you expect it to?
I agree with the advice above to go talk to the professor, who can help you focus your efforts so that you're spending the majority of your practice time working problems similar to those that are going to appear on the exam.
posted by BrashTech at 9:59 AM on April 10, 2013 [1 favorite]
It wasn't clear from your description what the duration of the course is, and whether you do the homework as the weeks progress, or in a huge chunk of study time just in the week before the exam. I think the best approach would be to do the homework during progressively during the course rather than cramming, if that's what you're doing.
posted by FrereKhan at 10:28 AM on April 10, 2013
posted by FrereKhan at 10:28 AM on April 10, 2013
I agree with a lot of the answers above--making sure you really understand why you got things wrong, making sure you can recognize and understand the concepts, and taking a critical look at your answers to make sure they make sense in a general way.
You may also want to look at your time management. Did you feel pressed for time on the test? Did you have enough time to go back and check your answers? It does no good for you to be the best 20-minute problem solver and triple-checker if you only have 5 minutes per problem. You might benefit from doing some problems with the same constraints as the test, using the first test as a model.
posted by The Elusive Architeuthis at 12:23 PM on April 10, 2013
You may also want to look at your time management. Did you feel pressed for time on the test? Did you have enough time to go back and check your answers? It does no good for you to be the best 20-minute problem solver and triple-checker if you only have 5 minutes per problem. You might benefit from doing some problems with the same constraints as the test, using the first test as a model.
posted by The Elusive Architeuthis at 12:23 PM on April 10, 2013
Also, dude, Calc's flipping hard. I had a similar experience in Calc II - it became a personal battle that I had to make an A in the class, and I just couldn't do it. I made almost 100% in Calc I, but somehow in Calc II I would just always make simple mistakes on those tests, despite feeling like I understood it. It was the closest I came to losing my shit in college, and I think I was too hard on myself. Sometimes you just can't make it click. I'm not trying to discourage you from keeping on trying (10hrs/day!?), but if you make a B, eh. You're human, it doesn't really matter that much, and we could all probably use some humility anyway.
posted by Buckt at 6:36 PM on April 10, 2013
posted by Buckt at 6:36 PM on April 10, 2013
A few questions:
- How much time do you spend on your Calc II coursework when it's not the week before an exam (as in just doing homework and any other general review)?
- How long (in hours) does it take you to one problem set (homework assignment)?
- How often are homework assignments collected (if at all)?
- When doing the homework, what do you spend the bulk of your time on? Understanding the problem? Setting up the problem? Doing calculations? Checking your work?
- Specifically what kind of errors have you been making on exams? Are you making the same types of mistakes? See http://www.math.vanderbilt.edu/~schectex/commerrs/ for some ideas about errors.
When you speak with the professor -- so glad you're going to do this! -- you might want to ask him or her about how long assignments/studying should take. I've had several professors that subscribed to the Rule of 3: they would find out how long it would take them to do an exercise and then multiply that by three to figure out how long it should probably take a student to do it. He or she may be able to point you to tricks that will make your work more efficient time-wise.
Seconding the suggestion to do similar problems instead of redoing your homework for studying.
If you aren't doing so already, consider sketching out each problem before setting it up. Draw a picture of the function and its axis of rotation, label your upper and lower limits,
your delta x (or y), etc. Seeing what you're doing can help.
Also, reading the questions aloud and then talking through your solutions might help for studying. Mathematics is a language and sometimes speaking it aloud helps to make connections (and avoid errors). Come exam time, read the questions to yourself in your head.
posted by wiskunde at 9:01 PM on April 10, 2013
- How much time do you spend on your Calc II coursework when it's not the week before an exam (as in just doing homework and any other general review)?
- How long (in hours) does it take you to one problem set (homework assignment)?
- How often are homework assignments collected (if at all)?
- When doing the homework, what do you spend the bulk of your time on? Understanding the problem? Setting up the problem? Doing calculations? Checking your work?
- Specifically what kind of errors have you been making on exams? Are you making the same types of mistakes? See http://www.math.vanderbilt.edu/~schectex/commerrs/ for some ideas about errors.
When you speak with the professor -- so glad you're going to do this! -- you might want to ask him or her about how long assignments/studying should take. I've had several professors that subscribed to the Rule of 3: they would find out how long it would take them to do an exercise and then multiply that by three to figure out how long it should probably take a student to do it. He or she may be able to point you to tricks that will make your work more efficient time-wise.
Seconding the suggestion to do similar problems instead of redoing your homework for studying.
If you aren't doing so already, consider sketching out each problem before setting it up. Draw a picture of the function and its axis of rotation, label your upper and lower limits,
your delta x (or y), etc. Seeing what you're doing can help.
Also, reading the questions aloud and then talking through your solutions might help for studying. Mathematics is a language and sometimes speaking it aloud helps to make connections (and avoid errors). Come exam time, read the questions to yourself in your head.
posted by wiskunde at 9:01 PM on April 10, 2013
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posted by chickenmagazine at 8:54 AM on April 10, 2013 [4 favorites]